Title: A NonHolonomic Control System
1A Non-Holonomic Control System
2The Aim
- To produce a system capable of following a smooth
path through a small number of variables. - This system should be capable of being used on
any robotic system, particularly non-Holonomic
situations. - This system should be able to adapt the smooth
path, whilst, when possible, retaining smoothness
in the event of unforeseeable circumstances.
3An Example
A robot navigating non-holonomically from one
position and orientation to another along a
smooth path, when a global map of the environment
is unavailable. If obstacles should be
encountered, the system should be able to adapt
its configuration path to avoid the obstacles,
whilst still proceeding towards the goal.
4Navigation
5The General Method
- A spline is calculated connecting the initial and
end conditions - A nearby subgoal is set some way along this
spline. - The subgoal is approximately attained via
gradient descent of the control parameters - The spline then adapts to compensate for the
actual configuration state realised. - Further subgoals are then set and attempted until
the goal is attained.
6Subgoal Chaining
Finish
Path
Subgoal
Start
7Adaptation
Finish
Adapted Spline
Original Spline
Old Subgoal
New Subgoal
Start
Actual Path
8The Initial Non-Holonomic Task
- Rolling Disc
- Control the movement of a rolling disc
- Along a smooth path
- From one x, y, and orientation, to another.
- Control Parameters
- Roll
- Spin
9The Rolling Disc
10What are non-Holonomics?
- Essentially controllable non-Holonomics are that,
whilst all positions and orientations may be
realisable, all paths are not. - For example, imagine a car, whilst it is possible
for it to be in any position on the road, it is
not possible for it to move sideways.
11Non-Holonomics
- Start and end parameters do not define the
solution - Only certain configuration paths are possible
- The configuration resulting from a given control
variation may be known, but the control sequence
resulting in a desired configuration state is
not. - Finding a correct sequence of changes in control
parameters dynamically, is essential for the
solution - The correct actions, in the wrong sequence will
not result in success - Recognised as difficult to solve!
12Non-realisable Path Example
13Attempts so far
- Several issues attacked through continually
refined strategies - No complete success so far, but enough to ensure
publishable steady progress - System has been in development for 9 months
14Euclidean Distance Method Principle
- Intuitive
- Distance from current state to the goal
- Decreasing the distance decreases the error
- System is drawn towards the goal
15Euclidean Distance Problems
- High Strain Paths
- The ideal spline is not adhered to
- Occasional phenomena
- Reversing
- Reverse Parking
16High Strain Path
17Strain Method Principle
- The spline plots the minimal strain path
- This is how smoothest path is defined
- Therefore calculating the strain of the proposed
path, and using strain in the gradient descent
process, will encourage the smoothest path to be
produced when the ideal spline is not realisable
18Strain Method Problems
- Bad error surface
- Ravine effect at goal
19Current Status
- 2 Systems
- A fixed spline can be followed, when realisable,
with constant disc movement - A spline can be followed in an adaptable manner,
when realisable, though with non-constant disc
movement.
20Current System 1
- Euclidean Distance based
- The spline is fixed, until proven necessary to
adapt - Therefore the subgoals are fixed
- Therefore low strain path is produced
- Strength Constant Movement Possible
- Weakness non-adapting spline
21Current System 2
- Euclidean Distance based
- Spline adapts
- Therefore low strain path is produced
- Strength constantly adapting spline
- Weakness Requires Stop and Think
22Current Aim
- To make the adaptable spline capable of constant
disc movement - Either remove stop and think from 2
- Or develop good trigger system for 1
23The Future (6-12 months)
- Finish the Rolling Disc problem
- Obstacle avoidance
- Differential drive
- Tackle problems with unrealisable smooth paths,
through techniques such as strain potential
24The Future (Grand Plan)
- Generic smooth motion demonstrated through robots
capable of major types of challenging motion. - E.g.
- Obstacle Navigation
- Non-Holonomic Motion
- Dynamic Stability